Productivity: What Is It, and Why Do We Care About
It?: Disaggregation by Source and Sector Yields Important
Insights.

Subject:

Production (Economics)
(Economic aspects)

Authors:

Steindel, CharlesStiroh, Kevin J.

Pub Date:

10/01/2001

Publication:

Name: Business Economics Publisher: The National Association for Business Economists Audience: Academic; Trade Format: Magazine/Journal Subject: Business; Economics Copyright: COPYRIGHT 2001 The National Association for Business Economists ISSN:0007-666X

Issue:

Date: Oct, 2001 Source Volume: 36 Source Issue: 4

Product:

Product Code: E400000 Production & Business Activity

Geographic:

Geographic Scope: United States Geographic Code: 1USA United States

Accession Number:

80924109

Full Text:

Economists, business analysts, and policymakers have all focused
considerable attention on U.S. productivity growth in recent years. This
paper presents a broad overview of productivity--both labor and total
factor--and discusses why it is such an important topic. We begin with
the official U.S. productivity statistics prepared by the U.S. Bureau of
Labor Statistics and discuss several stylized facts. We show how
productivity relates to critically important variables like long-run
growth, living standards, and inflation. We then describe the proximate
factors that determine labor productivity using a standard growth
accounting framework. Finally, we outline a series of unresolved
productivity issues that have direct implications for the future of the
U.S. economy.

Recent years have seen widespread discussion of productivity, and
for good reason. It appears that U.S. labor productivity growth has
improved sharply, perhaps approaching the pace of the "golden
age" of the 1950s and 1960s. To put the importance of this recent
change in perspective, consider the direct impact. If labor productivity
were to grow at 1.4 percent per year (the average rate from 1973 to
1995), output per hour would rise by 33 percent after twenty years.
Growth of 2.4 percent (the average for 1995-2000) implies that it would
be 64 percent higher after twenty years. Clearly, the rate of
productivity growth can have an enormous effect on real output and
living standards. (1)

The debate about the sources and sustainability of the recent
productivity revival has often hinged on somewhat obscure concepts such
as "cyclical" and "trend" components of
productivity; differences between "labor" and "total
factor" productivity; and the relative importance of factors like
"capital deepening," "spillovers,"
"productivity of computer output," and "productivity of
computer use." Many of these terms are not only similar in wording,
but the intellectual differences between them can also be quite subtle.

This paper aims to elucidate the key ideas and concepts in the
economic analysis of productivity and apply them to recent trends. We
begin by describing the most commonly used measures of productivity,
discuss the importance of productivity for several major economic
variables, sketch some of the factors believed to determine
productivity, and finally note several open research questions in this
area.

What is Productivity?

This section discusses the measures of productivity that are most
widely used by economists and business analysts and reviews their most
noteworthy empirical characteristics. We start with the most basic
concept of labor productivity-defined simply as real output per hour of
work. We then deal with the more difficult concept of total factor
productivity--defined as real output per unit of all inputs. This
reflects, in part, the overall efficiency with which inputs are
transformed into outputs and is often associated with technology, but it
more accurately reflects the impact of a host of other factors like
efficiency gains, economies of scale, any unaccounted inputs, resource
reallocations, and others. Finally, we review some limitations of these
measures.

Labor Productivity

Perhaps the most noted measure of productivity is the Bureau of
Labor Statistics' (BLS) series on output per worker-hour for the
private non-farm business economy, an index of labor productivity (BLS,
2001b). Similar measures have been calculated since the 1800s, when
Congress expressed concern that human labor was being replaced by
industrialized machinery--not so different from the concerns of some
workers today!

We first examine the evolution of labor productivity in the
post-war period. The four-quarter change in private non-farm labor
productivity is plotted in Figure 1. (2) Two features stand out. First,
labor productivity growth has an obvious cyclical component: low or
negative during recessions and high in the early stages of expansions.
This procyclicality of productivity is well known and largely reflects
the lack of instantaneous adjustment in factor markets. (3)

Second, looking beyond the cyclical movements, labor productivity
growth was decidedly lower in the twenty years or so starting in the
early 1970s than in the earlier period. Despite considerable research,
this "productivity slowdown" remains largely unexplained. (4)
From 1996 onwards, however, there has been a sharp strengthening in
productivity growth to rates similar to the earlier period. From 1959 to
1973, non-farm business productivity grew 2.7 percent per year, then
dropped off to 1.4 percent per year for 1973 to 1995. From 1995 to
mid-2001, however, productivity growth averaged 2.4 percent per year.
(5)

The non-farm business series is only one of many measures of labor
productivity produced quarterly by BLS. BLS also regularly produces
measures of output-per-worker hour for all private business (adding back
the farms), for non-financial corporations, for manufacturing as a
whole, and for the durable and non-durable components of manufacturing
separately. These series are published quarterly (BLS (2001b)), and are
available at http://www.bls.gov/lprhome.htm.

The manufacturing labor productivity series is shown in Figure 2.
The growth of labor productivity in manufacturing is typically
significantly higher than that for all of non-farm business, but
exhibits a similar procyclical pattern. Manufacturing productivity
growth also slackened somewhat in the 1970s, although its rebound began
earlier than that for all business and has been much more pronounced.
Measured manufacturing productivity growth in recent years has been even
stronger than in the 1950s and 1960s, with an annual rate of 4.4 percent
per year since 1995 compared to 2.6 percent for 1958-73 and 2.7 percent
for 1973-95

A related broad measure of labor productivity produced by the BLS
is for non-financial corporations (Figure 3). This series has gained
some attention in recent years, for example, Corrado and Slifman (1999),
in part because the data from this very large sector may be better than
elsewhere. Output in the financial sector is, by definition, excluded
from it; and other sectors that are quite difficult to measure--such as
construction, medicine, education, and law--are smaller parts of the
corporate sector than they are of the economy as a whole. Figure 3 shows
that non-financial corporate productivity did not show as pronounced a
slump in the 1970s and 1980s as did non-farm business productivity.
Moreover, in the 1990s, its growth rebounded to a faster pace than in
the 1960s. Here, too, is a rebound in productivity after 1995.

A final set of disaggregated labor productivity data is maintained
by the BLS Division of Industry Productivity Studies, which now
publishes labor productivity measures for over 500 3-digit and 4-digit
industries, as defined by the Standard Industrial Classification (SIC)
system. This program includes annual estimates of labor productivity for
certain manufacturing, service-producing, and mining industries.
Currently, the data are available through 1999, and the series are
updated periodically as new data become available.

Data from the Bureau of Economic Analysis (BEA) can also be used to
produce labor productivity estimates, which differ in certain respects
from those of BLS. BEA produces output data at roughly the two-digit SIC
level in their "gross product originating" (GPO) database,
which measures each industries' contribution to gross domestic
product (Lum and Moyer (2000)). These data are available in both current
and chain-weighted dollars. BEA now also makes "gross output"
data available for all industries. We discuss differences between the
GPO and gross output concepts below. BEA uses a different concept of
labor than BLS; instead of hours worked they provide estimates of
full-time equivalent workers. The BEA real output data can be divided by
the BEA's labor series to derive either aggregate or industry labor
productivity series. Like the BLS industry productivity series, (6) the
BEA industry data are only available annually; and there are
considerable lags in their construction, due to the difficulties in
compilin g the employment data and the detailed data by industry. (7)

Total Factor Productivity

All the series described so far relate to the productivity of
labor, defined as output per hour worked or per employee. As discussed
in more detail below, in order to understand the growth of labor
productivity, it is sometimes helpful to look more deeply at the data to
the contributing factors. To this end, economists have developed methods
to measure the contributions to labor productivity from measurable
factors such as changes in the educational achievement and experience of
the workforce, and changes in the amount and composition of capital with
which labor works.

Any remaining portion of productivity growth left unaccounted for
(i.e., the residual amount of output growth not explained by measured
input growth) is usually called "total factor productivity"
(TFP). (8) Presumably, total factor productivity growth reflects
phenomena such as general knowledge, the advantages of particular
organizational structures or management techniques, reductions in
inefficiency, and reallocations of resources to more productive uses. We
return to the details of TFP calculations in the following section.

The BLS regularly produces annual estimates of total factor
productivity growth for large sectors of the economy, e.g., the private
business and non-farm business sector (BLS (2001a)). BLS also produces
regular estimates for manufacturing and eighteen component two-digit SIC
industries within manufacturing, but it does not regularly publish total
factor productivity estimates for either the service sector as a whole,
or for individual service industries. Gullickson and Harper (1999)
provide estimates for recent periods based on unpublished BLS data for
certain non-manufacturing industries. The BLS industry productivity
program produces TFP estimates for more detailed manufacturing
industries and for railroad transportation with some lag.

The BLS total factor productivity series for all nonfarm business
is illustrated in Figure 4. In general, broad movements in this series
are similar to those in labor productivity; higher in the 1960s and late
1990s than in the intervening period. Other estimates are also made of
total factor productivity growth; estimates in Jorgenson and Stiroh
(2000) and Oliner and Sichel (2000), for example, are broadly similar to
the available BLS numbers..

Difficulties in Measuring Sectoral and Industry Productivity

It may be surprising that data on productivity, particularly total
factor productivity, in large sectors or major industries is so scarce.
The problems with compiling such data are both practical and conceptual.
On a practical level, detailed sectoral or industry data on output and
inputs (including labor) can be problematic; sampling problems that wash
out at the aggregate level appear in full force when individual
industries are examined.

The conceptual problems with examining disaggregated data are also
severe. They relate primarily to the definition of "output."
There are two standard concepts of output in the economics literature:
value added (also called gross product originating) and gross output.
Gross output equals the total value of sales and other operating
receipts of an economic unit, while value added subtracts from gross
output the value of goods and services purchased from other units that
are used in the course of production (intermediate inputs). The BLS
non-farm business sector and BEA GPO data are value-added concepts,
while the manufacturing total factor productivity estimates are based on
a gross output concept. (9)

Value added is an attractive measure because it is fairly easily
measured in current dollars: the current dollar value added of an
economic unit is its current dollar income (payments to labor and
capital), which is observable from tax data. Current dollar value added
summed across all industries, therefore, has the nice property that it
equals GDP when all economic sectors are included. However, value added
can be difficult to measure in constant dollars, since, in principle,
sales and inputs should be deflated by separate price indexes.10 In
particular, deflation of inputs is problematic because the mix of
services inputs used by an economic unit can vary considerably. While
BEA currently employs a "double deflation" method for all
private industries to measure real value added, (11) the reliability of
the estimates for any one industry can affect those for many others.

Gross output per worker is closer to the ordinary notion that
productivity is measured as sales per worker. Real gross output may also
be easier to measure than real value added because it depends largely on
deriving price indexes for observable sales. Furthermore, it may be a
conceptually more valid measure for productivity analysis than value
added because it will not be distorted by changes in the mix of primary
and intermediate inputs. (12) Care must be taken when analyzing the
impact of industry or sectoral trends in gross output per worker for the
economy as a whole, however, since the sales of many entities are
intermediate inputs to other sectors and not part of final demand or
GDP, which is a value-added concept.

Why is Productivity Growth Important?

The interest in productivity statistics reflects the belief that
they are related to a number of things that are important to economists,
business, and policymakers, such as overall economic growth, growth in
real per capita incomes, and inflation.

Productivity Growth and Economic Growth

The relationship between labor productivity growth and economic
growth would seem to be obvious. Output growth is, by definition, the
sum of the growth of hours and labor productivity growth. (13) Hence,
higher productivity growth would appear to be associated with higher
output growth. Of course, for periods as long as decades, demographic
forces differ substantially, which affects the growth of labor input and
aggregate output independently of productivity trends.

Perhaps surprisingly, the simple link between output and
productivity growth is not completely reliable at aggregate levels in
the U.S data. Figure 5 plots the growth rate of real non-farm business
output and labor productivity for each decade and each hall-decade from
the 1960s to the 1990s. From decade to decade there is a strong
consistent relationship between swings in labor productivity growth and
swings in output growth. For example, output growth slowed substantially
in the 1970s and 1980s as labor productivity growth slowed, while output
growth improved in the l990s as labor productivity growth rebounded.

The relationship between productivity and aggregate output growth
seems somewhat looser when we move from decade to hall-decade data. The
strongest period for productivity growth (1960-64) is not the strongest
period for output growth; the weakest period for productivity growth
(1985-89) is not the weakest period for output growth. In all
likelihood, this loosening occurs because there is considerable
non-demographic variability in hours worked across five-year periods.
Business cycle forces heavily affect the demand and supply for labor, so
the resulting cyclical swings in the quantity of labor can either
augment or reduce the output effects of productivity fluctuations. The
strength of the business cycle varies considerably when looking across
half-decades; moreover, the configuration of these forces can change
from cycle to cycle. Over the course of a decade, however, business
cycles tend to smooth out as does the growth of labor. This smoothness
in labor force should become more pronounced as the time fre quency
lengthens, hence very long-run projections of the economy such as those
produced by the Congressional Budget Office (CBO, 2001a, 2001b)
essentially reflect demographic and productivity assumptions.

The effect of timing on the relationship between productivity
growth and output growth is shown more extensively in Figure 6, which
plots the correlation between the two series from one to forty quarters.
The correlation is quite high at one quarter, then falls off rapidly, is
flat up to five years (twenty quarters), and then rises. This pattern
suggests that there are two types of connections between productivity
growth and output growth--the long run or "demographic"
relationship, and a very short-term or "cyclical" one.

The very strong short-run relationship between output and
productivity suggests that it is still difficult to compute the true
magnitude of the late-1990s revival in trend productivity. Real output
growth has also strengthened in this period, and it is possible that
some of the improvement in productivity will disappear from the data if
and when output growth slows. Robert Cordon (1999, 2000), for example,
has argued that much of the recent productivity gains are cyclical in
nature and will likely fade when the economy slows.

Productivity Growth and Per-Capita Income Growth

Standard textbook economics asserts that productivity growth and
the growth of real wages are equal. Quite often this proposition is
stretched to make the claim that productivity growth equals the growth
of real percapita income. In reality, the relationship between
productivity and income is not that tight-particularly over the short
run. A standard measure of real per capita income is constant-dollar per
capita disposable income, where the personal consumption expenditures
(PCE) deflator is used as the price measure. The correlations between
this income measure and productivity growth for periods from one quarter
to ten years are shown in Figure 7. The short-term correlation is quite
weak, but grows steadily as the interval increases.

There are many reasons why the short-term correlation between
productivity growth and income growth could be weak. On a conceptual
level, the theoretical link between productivity and real wages strictly
holds only if an economy produces one good using a
constant-returns-to-scale production technology. These
requirements--especially the "one-good" assumption--hardly
strictly hold for the US economy! The multiplicity of produced goods
means that there will likely be a divergence between growth in the
output price deflator (used to compute productivity and real wages) and
growth in a consumer product price series (used to compute real
incomes). Furthermore, there is considerable slippage between growth in
wages per hour, and growth in income per capita. There is more to income
growth (especially on an after-tax basis) than growth in wages or even
overall compensation, and there is not a fixed relationship between
hours worked and population due to fluctuations in unemployment, labor
force participation, and hou rs worked per person.

Over the longer run, many of these slippages should lessen in
importance; the differences between output and consumer prices lessen,
growth in after-tax income and compensation look more alike, and growth
in hours and population converge. Thus, the correlation between
productivity and real income increases as the time period examined
lengthens, and the adage that productivity growth is the key to income
growth is increasingly supported.

Productivity Growth and Inflation

Some macroeconomists are fond of the saying "inflation is
always and everywhere a monetary phenomenon." Productivity growth
is the epitome of a non-monetary phenomenon: as we will discuss below
its two main determinants are believed to be capital formation and the
evolution of technology. It is not clear that there should be any stable
relation between inflation and either capital formation or technological
change, so inflation and productivity could be unrelated. Nonetheless,
the data appear to show linkages between productivity growth and
inflation.

The correlation between productivity growth and inflation, measured
by the chained price index for GDP, (4) is shown for frequencies from
one quarter to ten years in Figure 8. The one-quarter correlation is
negligibly small, but as the interval increases the magnitude of the
relationship grows. The (negative) correlation is smaller than for
output growth or real income, but it persists at a fairly stable level
through the longest frequency examined. It seems to be the case that
periods of higher productivity growth are periods of lower inflation.

If productivity growth is inherently a "real" phenomenon,
and inflation is inherently a "monetary" phenomenon, why
should there be such a relationship? One possibility is that the
causation goes from inflation to productivity growth; higher inflation
rates could distort the price mechanism and may be associated with
reduced efficiency throughout the economy. In other words, inflation may
have a negative impact on capital accumulation or technical change.
Another explanation may be that periods of high productivity growth,
since they are periods of relatively fast output and real income growth,
are the times in which it is easier for monetary authorities to pursue
anti-inflationary policies. If positive productivity surprises act as
positive supply shocks, then monetary policy can be restrictive with
fewer effects on real variables. (15) However, if negative surprises act
as negative shocks, expansive monetary policy is likely to lead to
inflation.

For instance, it is arguable that the unexpected decline in
productivity growth in the 1970s was a major factor behind the
contemporaneous increase in inflation. In that decade, downward
pressures on real output and income growth from reduced productivity
growth complicated the environment for anti-inflationary policies. This
view was concisely summed up in the 1979 Economic Report of the
President, which stated "Productivity growth in 1978 showed a very
marked slowdown from accustomed rates, adding substantially to
inflationary pressures and raising fundamental concerns about underlying
trends (Council of Economic Advisers, 1979, p. 67)." Likewise, the
mirror image of faster productivity trends in the late 1990s may have
helped create an environment favorable to reductions in inflation.

VAR Evidence on Linkages

The above interpretations of the simple correlations between
productivity and output, income, and inflation in the preceding
discussion are clouded by the presence of other factors that jointly
influence the variables. One simple way to correct for these effects--at
least for common trends--is to examine impulse response functions
computed from vector auto regression (VAR) systems that relate
productivity growth to each of the other variables. The responses relate
impulses (changes in a variable not accounted for by recent movements in
itself and the other variable) in productivity growth to growth in
output, real income, and inflation, as well as those relating impulses
in the three latter variables to productivity growth.

These impulse responses, estimated from the three bivariate
systems, are shown in Figure 9, along with two-standard-error bands
surrounding the point estimates. There is clearly a sharp
bi-directional, short-term relationship between productivity impulses
and output growth, and between output impulses and productivity growth.
These relationships quickly fall off and are consistent with the simple
correlation between output growth and productivity growth being high at
one-quarter, but weakening as longer intervals are examined. The
short-term impulse response relations from productivity to real income
and inflation, and from real income and inflation to productivity, are
weaker in magnitude and also consistent with the simple correlations.

What Factors Determine Productivity Growth?

We next identify the factors that are believed to determine labor
productivity to better understand how it evolves. We begin with a
traditional "sources of growth" analysis that decomposes labor
productivity growth into three primary components--capital deepening,
labor quality, and total factor productivity. This approach has been
used in much applied productivity work. For example, BLS (2001a)
provides the official U.S. productivity history; CBO (2001a, 2001b) and
Council of Economic Advisors (CEA, 2001) project U.S. growth; and Gordon
(2000), Jorgenson and Stiroh (2000), and Oliner and Sichel (2000)
examine the impact of information technology, all using this traditional
growth accounting approach.

While this methodology provides valuable insights on the growth
process, there are also several well-known caveats that deserve mention.
Most important, this approach accurately quantifies the proximate
sources of growth like capital accumulation and hours worked, but it
cannot really identify the deeper forces that determine those variables.
This requires a more fully developed model of consumer preferences, firm
decisions, and policy variables. Moreover, total factor productivity
growth--often interpreted as a proxy for technology--is an important
force that remains exogenous to the framework and essentially
unexplained. (16) With these caveats in mind, we move to the details
beneath a neoclassical growth accounting analysis.

Traditional Sources of Productivity Analysis

We begin with an aggregate production function that relates output
to the primary inputs, capital and labor, as well as the level of
technology available in each period. Under standard assumptions that all
inputs are paid their marginal product and all income is paid out to
primary inputs (input exhaustion), one can mechanically derive the
following relationship for labor productivity growth, d In(Y/H):

where Y is real output, H is hours worked, [v.sub.k] is
capital's share of national income, K is the flow of capital
services, L is labor input, and A is total factor productivity.
Jorgenson and Stiroh (2000) provide details.

Equation (1) relates labor productivity growth to three factors,
described in more detail below. The first term is capital deepening. The
second is a labor quality effect that measures productivity gains as
firms substitute towards workers with more skills and higher marginal
products. Labor productivity grows in proportion to the growth in
capital and to the growth in labor quality, which is defined as the
growth in labor input per hour worked. The final factor is total factor
productivity (TFP), a catchall term that captures the impact of
technological change, as well as increasing returns to scale, efficiency
gains, omitted variables, reallocations from low to high productivity
activities, and any remaining measurement error.

We now discuss how each of these three factors can be estimated.
The methodology is well established and recent applications can be found
in BLS (2001a), Jorgenson and Stiroh (2000), and Oliner and Sichel
(2000). While there are some differences across studies, we briefly
review what might be considered best practice in this area. BLS (1997a)
provides details on the procedure and data sources used in the BLS
calculations.

Capital Deepening

Capital deepening reflects the increase in the amount of services
from physical capital available to each worker. As firms invest and
purchase new equipment and structures, the workforce becomes better
equipped and is able to produce more output; hence, productivity growth
rises proportionally with capital deepening. (17)

As can be seen from Equation (1), there are three pieces of data
required to estimate the capital deepening term--capital's share of
nominal income ([v.sub.k]), the flow of capital services (K), and hours
worked (H). It is relatively easy to measure hours worked and
capital's income share; the former are available directly from the
BLS and the latter is available from national income data from the BEA.

The more difficult methodological question is how to properly
measure the amount of capital services available for production. This
topic has received considerable attention by economists, and we review
what has become the standard methodology. (18) In particular, we discuss
two specific issues--how to treat individual assets whose productive
characteristics are rapidly changing over time, arid how to correctly
aggregate different types of capital into a single number that
adequately captures the productivity attributes of all component assets.
Both are fundamentally questions of accurately measuring capital as a
factor of production and are central to production theory.

We begin with the issue of assets that are steadily becoming more
productive over time. Firms purchase new capital goods each year through
their investment in plant, equipment, and structures, so the business
investment data produced by the BEA is the appropriate starting point
(BEA (1998), Herman (2000)). Given information on decay and retirement,
one can estimate the stock of capital for each distinct type of asset
through the perpetual inventory method:

[S.sub.i,t] = [I.sub.i,t] + (1-[[delta].sub.i]) [S.sub.i,t-1] (2)

where [S.sub.i,t] is capital stock, [I.sub.i,t] is investment, and
[[delta].sub.i] is the physical depreciation rate for asset i at time t.

The perpetual inventory method gives the familiar interpretation of
the capital stock as a weighted sum of past investments, with weights
determined by the efficiency profile of capital of different ages. (19)
Implicit in this approach is the assumption that investments in a
particular asset from different years are perfect substitutes for one
another. Given the enormous quality change in certain assets like
computers, this may seem unreasonable at first glance. This problem is
well-known, however, and both BEA and BLS spend considerable resources
to develop the appropriate data to deal with it.

BEA now employs "constant-quality" price deflators for
many assets with rapid quality change over time. In essence, these
deflators measure the price of a bundle of productive characteristics
over time rather than the price of a particular unit. This translates
quality improvements across different vintages of investment into
increases in the quantity of homogeneous "efficiency units."
As a concrete example, consider how real computer investment is measured
when current models are much more powerful than earlier ones, e.g.,
faster, processors, larger hard-drives, more memory, etc. The observed
purchased price of a computer system has not changed very much, so large
improvements in performance imply the price of these productive
characteristics has fallen. As a consequence, the official price index
for computers has fallen rapidly, nearly 30 percent per year for
1995-99, while the real quantity of investment has exploded. Thus,
correct deflation of nominal investment accounts for quality
improvements in a part icular asset over time. (20)

Given the constant-quality deflators and depreciation rates,
Equation (2) describes the evolution of the productive stock of capital,
measured in consistently defined efficiency units, for each asset. Not
all investment goods and capital assets are the same, however, and one
must account for this heterogeneity to construct an appropriate measure
of aggregate capital input used by an industry or economy. Information
technology assets have high marginal products and relatively short
service lives, for example, which makes them quite different from
long-lived assets like non-residential structures.

To account for these differences, most recent studies incorporate a
"capital services" methodology. This approach, developed by
Jorgenson and Griliches (1967), creates an aggregate measure of capital
services by using each asset's marginal product to determine the
appropriate weight. Assets with higher marginal products receive larger
weights. The main practical concern is how to estimate the marginal
product for each type of capital needed for weights, and for this one
can turn to economic theory for guidance.

Consider the firm's investment decision where it is choosing
between buying a productive asset or some alternative investment
opportunity. To be an equilibrium, the firm should be just indifferent
between two alternatives: investing the money ([P.sub.i,t-1]) and
earning a nominal rate of return, or buying the piece of capital with
the same amount of dollars, collecting a rental fee (or equivalently,
profiting from the use of the asset for a period), and then selling the
depreciated asset at next period's price ([P.sub.i,t]). This
implies the following equilibrium condition:

where [i.sub.t] is the nominal interest rate, [P.sub.i,t] is the
acquisition price, and [c.sub.i,t] is the rental or service price for
asset i at time t. Rearranging yields the familiar "cost of
capital" or "user cost" equation:

where [[pi].sub.i,t] is the percent change in the acquisition
price. (21)

Equation (4) can be evaluated for each asset to produce an estimate
of an asset-specific cost of capital, [c.sub.i,t] which equals the value
of the marginal product of the asset under the neoclassical assumptions.
To better understand the economics of the cost of capital equation,
again consider the case of computers. Measured in constant-quality
efficiency units, computer prices have fallen rapidly ([[pi].sub.i,t] is
large and negative) and computers depreciate quickly ([[delta].sub.i,t],
is large and positive), [c.sub.i,t] is large and positive. Computers
must have a large service price and correspondingly high marginal
product value to compensate for large capital losses and rapid
depreciation.

These service price estimates directly affect the aggregate measure
of capital since they serve as aggregation weights for different types
of capital. (22) A comparison between the growth of capital services,
which uses the cost of capital as the weight for each asset, and the
growth of the capital stock, which uses the acquisition price as the
weight is shown in Figure 10. The index of capital services grows much
faster (4.2 percent per year) than the index of capital stock (3.2
percent) for the period 1959 to 1998. This divergence is particularly
strong in the later periods and represents the substitutions towards
short-lived assets, like computers and other information technology,
with relatively high marginal products. Failure to account for the
relatively high marginal product would understate the growth in
productive capital services.

Labor Quality

Growth in labor quality captures the increase in labor input from a
changing mix of workers. As the workforce evolves and workers with
different skills and marginal products are employed at different rates,
this change in composition directly affects how much output can be
produced from a given quantity of worker hours. For example, as relative
wages change, firms substitute between different types of workers; and
this changes the average productivity of the workforce. This composition
effect is often referred to as a change in labor quality.

To be more precise, recall that Equation (1) defines labor quality
growth as the difference between growth in aggregate labor input (L) and
aggregate labor hours (H). Estimates of labor hours are relatively easy
to obtain by summing the hours worked of all types of workers and
computing the growth rate. In this calculation, all types of workers are
essentially treated the same and receive identical weights.

A more difficult task is to construct an estimate of aggregate
labor input that accounts for the changing composition of workers.
Rather than simply summing hours of all types of worker, estimates of
aggregate labor input employ weights equal to marginal products. Like
the estimates of capital services, it is appropriate to account for the
heterogeneity across different types of workers in order to provide a
more accurate measure of labor input used in production.

Following economic theory, relative marginal products can be
inferred from observed wage differentials across classes of workers,
i.e., workers cross-classified by age, education, sex, industry, etc.
This can be done econometrically (BLS, 1997b), or by calculating the
relative wages of different types of workers directly (Ho and Jorgenson,
1999). These two approaches are conceptually similar, and it is really a
data decision about which is preferred. The common assumption is that
relative wages capture differences in the workers' productivity and
that the quality of a specific type of worker is constant over time.

Figure 11 plots the growth rate of labor input (L) and hours worked
(H) from 1959 to 1998. As discussed above, the difference in growth
rates between these two series reflects changes in the composition of
the workforce, often referred to as labor quality change. For the period
1959-98, growth in labor input exceeded growth in hours worked (2.1
percent vs. 1.6 percent), implying steady growth in labor quality due to
demographic factors and compositional changes in the workforce.

Total Factor Productivity

The third factor identified in the traditional sources of growth
analysis is total factor productivity (TFP) growth. TFP growth
represents the ability to produce more output from the same inputs.
Conceptually, this can he thought of as a shift in the production
function. TFP is often viewed as a measure of technological change, but
it also reflects additional factors like economies of scale, efficiency
gains, resource reallocations, and measurement error, as well as the
growth in disembodied technology.

At this point, it is important to be clear about how TFP growth is
actually estimated. Under the assumptions used to derive Equation (1),
TFP growth, d In A, is defined as

d ln A = d ln Y-[v.sub.k]d ln K-(1-[v.sub.k])d ln L (5)

Thus, TFP growth is not observed at all; rather, it is calculated
as a residual as the output growth not explained by weighted input
growth. This is consistent with the interpretation of TFP growth as a
shift in the production function, but it is also somewhat unsatisfying
since, as a practical matter, TFP growth is a catch-all term that
captures the impact of all growth factors not explicitly measured.
Investment in unmeasured inputs like research and development or any
mis-measured capital and labor inputs, for example, affect the measured
TFP residual.

Moreover, the TFP estimate derived from this approach gives a valid
estimate of technical change only under the assumptions of competitive
markets and input exhaustion. As pointed out by Hall (1988), Hulten
(2000), and others, if these assumptions fail, the traditional TFP
residual diverges from what the economist is really trying to measure.
Basu and Fernald (1997), however, argue that even if not a pure
indicator of technical change, measured TFP is a valuable welfare
indicator. Finally, even if correctly measured, this approach can only
quantify how the rate of technical change fluctuates; it cannot explain
why it changes. TFP growth is entirely exogenous to this framework, and
thus without an economic explanation in this standard neoclassical
model.

Recent Estimates

With this measurement framework in hand, we review how each factor
contributed to the resurgence of U.S. labor productivity growth. As
discussed earlier, there has been a tremendous revival in U.S. labor
productivity growth. After growing 1.4 percent per year from 1973 to
1995, annual U.S. business sector productivity growth jumped to 2.5
percent per year from 1995 to 2000 (BLS, 2001b). To move beneath this
number and understand the proximate sources of acceleration, we discuss
the decomposition results reported by BLS (2001a), Jorgenson and Stiroh
(2000) and Oliner and Sichel (2000) and examine each of the three
factors identified by Equation (1).

Table 1 reports the growth decomposition for 1973-95 and 1995-99
from the three studies. Given that the studies use the same basic
methodology and data sources, it is not surprising that they reach
similar conclusions. (23) Since 1995, output growth has accelerated by
nearly two percent per year, due largely to faster labor productivity
growth (up 1.0-1.2 percent), but also due somewhat to faster growth in
hours worked (up 0.6-0.8 percent). It is the acceleration of labor
productivity that is most striking and has the most important
implications for macroeconomists.

Moving beneath the labor productivity estimates, we find that these
gains primarily reflect more rapid capital deepening and faster TFP
growth. Both Jorgenson and Stiroh (2000) and Oliner and Sichel (2000)
emphasize that accelerated capital deepening is due in large part to the
recent boom in high-tech investment, particularly computer hardware. As
the relative price declines of these assets accelerated in the late
1990s, firms responded with massive investment and capital accumulation.
Similarly, both studies identify rapid technical progress in the
high-tech industries as a source of accelerating aggregate TFP growth.
As high-tech firms become increasingly able to produce more advanced
hardware, semiconductors, and software, their productivity rises and
drives aggregate TFP upward. These studies report that information
technology-related forces account for about one-half to two-thirds of
the acceleration in U.S. productivity. As a final point, there is little
change in the growth of labor quality in the lat e 1990s. This is
consistent with the notion of a very tight labor market as relatively
low-skill workers are drawn into the labor pool.

These traditional sources-of-growth studies show that the U.S.
economy in the late 1990s appears quite different from the prior two
decades. Technical progress, in particular, seems to have accelerated in
recent years, driving both TFP growth and inducing massive investment in
high-tech assets. As a readily acknowledged caveat, however, this type
of analysis cannot explain why technical progress accelerated in the
high-tech industries, which remains an important issue for economists
interested in the performance and organizational structure of these
industries. Nonetheless, this analysis is quite useful, because by
identifying the proximate sources of productivity growth, analysts can
better understand the growth process and can more effectively address
policy questions of how to stimulate growth.

Important Productivity Questions

We now apply the data and concepts described previously to some
current productivity issues discussed in the academic, policymaking, and
forecasting communities. All of these issues are unresolved, but
discussion is useful to understand the way answers may be obtained in
the future.

The Productivity Revival: Cyclical or Structural?

U.S. productivity growth clearly has a major cyclical component.
Overall economic growth strengthened substantially in the latter half of
the 1990s as the U.S. economy appeared to be growing faster than its
sustainable trend. It has been argued, especially in Robert Gordon
(1999, 2000), that much of the rebound in productivity growth in recent
years is a reflection of the strengthening of aggregate demand rather
than a fundamental improvement in the medium or longer-term productivity
trend. This cyclical argument has several facets.

The neoclassical growth accounting results presented in Table 1
suggest that much of the recent improvement in labor productivity growth
is due to faster capital deepening and an upswing in TFP growth. Capital
deepening itself has a normal cyclical component since investment is
highly cyclical, so the recent capital deepening may be less a factor
leading to faster productivity growth and more a consequence of faster
economic growth.

TFP growth is also highly cyclical (Figure 4). The cyclical
component of TFP growth likely reflects more intensive use of capital
and labor resources by firms when demand increases. In principle,
neoclassical growth accounting could pick up more intensive use of
existing resources, but in practice such swings are often chalked up to
fluctuations in TFP. (24) Thus, the ability of the neoclassical
framework to account for the recent increase in labor productivity
growth need not be inconsistent with the claim that much of the increase
is inherently cyclical.

Finally, the estimation framework discussed in the previous section
was developed to address the sources of growth over longer-terms. Over
shorter time periods, the quality of the data becomes an issue
(especially when dealing with the recent past, when much of the data is
subject to major revision, as has recently been the case), and the basic
assumptions used to derive the estimates may be questioned. Most
notably, the estimates of capital services are derived assuming that
output is produced using a constant-returns-to-scale technology, and
that markets for capital goods and financial instruments are in full
equilibrium, meaning that relative prices and financial returns provide
information about user costs in a straightforward manner. These
assumptions may be reasonable on average for long periods, but their
relevance for short periods (and in this context five years may be a
short period) can be questioned and therefore introduce additional
measurement error.

Fundamentally, then, we cannot dismiss the proposition that
cyclical forces, rather than true improvements in the underlying trend,
explain the recent improvement in productivity. This issue can only be
resolved by time, although recent developments are somewhat encouraging.
Non-farm business productivity rose 2.1 percent in 2001:Q2 even as
output in that sector fell (BLS, 2001b). Moreover, the four-quarter
increase in productivity ending in 2001:Q2 was 1.5 percent, which is a
fairly impressive increase, given that output growth over this period
was only 0.9 percent. In contrast, productivity rose only 0.7 percent
over the four quarters ending in 1995:Q2, a period in which output grew
2.9 percent. In addition, the rate of capital deepening has remained
quite strong--the growth of investment has slackened off, but its level
remains quite high--although we do not yet have the data to make a firm
estimate of TFP growth during the recent period of softer growth.

In addition, recent academic studies also suggest that the recent
U.S. productivity revival is not only a cyclical phenomenon. Basu,
Fernald, and Shapiro (2001), for example, suggest that the U.S.
productivity revival is a technological phenomenon and does not
primarily reflect factor utilization, factor accumulation, or returns to
scale. CEA (2001) and Stiroh (2001a) show that the industries that
invested most heavily in IT showed the largest productivity gains,
suggesting real gains from IT-use and are not only cyclical in nature.

Is Higher Productivity Growth Merely a High- Tech Phenomenon?

The official BLS data show that the recent strengthening of
productivity growth is most evident in manufacturing, and within
manufacturing it is most evident within the durable goods sector.
High-tech capital--for instance, computers, semiconductors, and
communication equipment--is produced within this sector. The annual BEA
data suggest that the fastest growth in productivity in recent years
(measured as gross output per full-time equivalent worker) has been in
the two-digit industries that produce these high-tech items. The
quality-adjusted prices of these goods have plunged in recent years,
which is another sign that productivity growth may be unusually rapid in
these industries.

Although Stiroh (2001a) shows evidence of a broad productivity
revival across many U.S. industries, the improvements in productivity in
other sectors have been somewhat more modest. These developments raise
two issues. First, can we really believe that the productivity
improvement is narrowly based? Second, is there a qualitative difference
between a productivity swing confined to a few industries and one more
broadly-based?

In our discussion of the neoclassical accounting of productivity
trends we noted that it is perfectly plausible to assume that the
productivity revival is unbalanced. In this framework, the high-tech
industries are experiencing a major boom in TFP growth, enabling them to
supply their products to the economy at much lower prices. The cheaper
cost of these capital goods has allowed acceleration in capital
deepening elsewhere, and induced a higher rate of labor productivity
growth. The issue is really why TFP gains are so narrowly focused.

This question is, almost by construction, irresolvable in the
neoclassical framework, where TFP is derived as a residual as the growth
that can't be attributed to observed factors. In the case of
high-tech industries it appears that true technological change is
driving TFP as these industries are able to continuously produce better
outputs at lower prices. As a practical matter, however, the attribution
of TFP growth to particular industries is fraught with potential errors
since it requires fairly detailed data on the inter-industry pattern of
intermediate input trade and resource utilization. Moreover, it may be
too soon to make sweeping conclusions about recent trends in industry
TFP growth; revised data may show higher recent growth in some
industries and lower in others.

Industry detail on productivity growth, however, may be less
important in weighing the benefits of faster productivity growth. Labor
productivity growth, no matter in what industry it occurs, allows the
existing workforce to produce more output in the aggregate. Faster TFP
growth, no matter in what industry it occurs, allows the existing
workforce and capital stock to produce more output in the aggregate.
Thus, if one is more interested in the growth of aggregate output and
less interested in the distribution of that growth (e.g., a fiscal
policy planner who needs to forecast future tax revenue) then breadth of
productivity gains may be less important. Of course, for other purposes,
like analysis of real wages and income distribution, this question may
be quite important.

Why is Productivity Growth So Slow in the Service Sector?

Productivity growth is disproportionately rapid in manufacturing
and in the non-financial corporate sector, which suggests that
productivity growth is disproportionately slow in the service sector.
Gorrado and Slifman (1999), for example, report that manufacturing labor
productivity grew 3.0 percent per year from 1989 to 1997, while service
sector productivity declined 0.9 percent per year. Similarly, Gullickson
and Harper (1999) estimate that total factor productivity in services
rose only 0.1 percent per year from 1977 to 1992. This contrasts with
the perception of important advances in production and distribution in
these services sectors. In addition, there has also been considerable
high-tech capital deepening, e.g., Triplett (1999) and Stiroh (1998)
show that the majority of computer capital is in service-related
industries.

Why, then, are the productivity measures so low? One potential
explanation is measurement error. It is reasonable to believe that there
are major problems measuring the output of many service industries, and
technological advances may have exacerbated these problems. This issue
has been raised by the BLS itself (e.g., Dean (1999) and Gullickson and
Harper (1999) as well as Diewert and Fox (1999)) and remains an
important research area for improving the national accounts.

For example, technology enables providers of financial and health
services to customize their offerings to individuals or firms. Such
specialization makes it extremely difficult to measure price indexes for
those industries. This erodes the reliability of the published real
output and productivity measures. The slow pace of productivity growth
in these and some other service sectors has led to widespread suspicion
that price inflation is overstated in these areas.

Few observers would doubt the likelihood that price inflation in
large parts of the service sector is overstated, and therefore
productivity growth is understated. The analytical significance of price
overstatement in the service sector, however, depends upon its size
relative to price overstatement elsewhere in the economy, and any change
in such overstatement over time. Differing degrees of price
overstatement across sectors will mean that the published data on the
distribution of productivity growth will be misleading, which could
hamper the design of effective policies to encourage true productivity
growth. Furthermore, since the service sector has been growing relative
to the rest of the economy over time, a relatively large price
overstatement means a progressively larger understatement of true
aggregate productivity growth; Griliches (1994) made this point in the
context of discussing the growing share of "hard-to-measure"
sectors. Sichel (1997), however, shows that even the growing share of
the servic e sector is not enough to substantially raise measurement
errors for the aggregate economy.

A worsening of measurement problems and an increase in the
overstatement in inflation in the service sector could compound this
problem, but the evidence is limited that any overstatement of service
sector inflation is growing over time. Steindel (1999) discussed the
quantitative consequences for aggregate productivity growth of
progressively growing overstatement of service sector inflation. He
found that, unless the problem is very severe (for instance, the
relative overstatement of inflation in the service sector has recently
increased by more than two percentage points a year), our basic
assessment of longer term aggregate productivity trends through the
mid-1990s would likely remain intact. However, if there is no
improvement in the relative overstatement of service sector inflation,
the understatement of aggregate productivity growth will worsen over
time.

It might be surprising, given the size of the service sector, that
its inflation overstatement does not look like it creates a major
distortion of the aggregate productivity data. When we look at the
details of the data, though, we find that the service sector share of
final product sales is considerably smaller than its share of say,
employment. Much of the service sector is devoted to providing inputs to
goods production (think of finance), and another large share is involved
in fairly straightforward activities such as transportation and power
supply, where problems in pricing output are probably not that large. As
pointed out by Baily and Gordon (1988), only a small portion of final
product in the private sector involves output of industries, such as
finance and health care, where it is plausible to argue that new
technologies could have increased inflation overstatement.

It appears that the problem of limited growth of service sector
productivity, if it actually is simply a data problem, involves mainly a
distortion of the pattern of productivity growth across industries. It
is possible that too high a fraction of productivity growth is being
attributed to goods production, and too little to the service
industries, and that advances in information-processing technology are
increasing this problem.

What is Sustainable Productivity Growth?

The recent experience with labor productivity growth projections
shows this to be a very difficult question. Consider the evolution of
the labor productivity projections produced by the CBO, which is
considered by some to reflect state-of-the-art methodologies. As
recently as 1998, CBO (1998) forecast potential labor productivity for
the nonfarm business sector to grow 1.7 percent per year through 2008,
slightly slower than the 1.9 percent average for 1949-97. As the U.S.
economy continued to outperform forecasts in recent years, CBO's
projections steadily evolved. CBO (1999) forecast 2.0 percent potential
labor productivity growth for 1998-2009, while the forecast in (2000a)
rose to 2.3 percent. In the most recent forecast, CBO (2001b) projects
2.5 percent potential labor productivity growth for the non-farm
business sector over the next decade, down from 2.7 percent at the
beginning of the year (CBO, 2001a). Clearly, estimating sustainable
productivity growth is not an easy task.

The decomposition of improved labor productivity growth into the
component due to capital deepening and TFP growth lets us begin to
answer this question. (25) In some sense, TFP growth can not be forecast
with accuracy precisely because it is a residual; if we knew the forces
that can be used to forecast it, we might be able to account for it in
the neoclassical framework. However, given the record of the last forty
years, reasonable bounds on trend TFP growth look to be zero (the trend
in the 1980s) to over one percent per year (the trend in the 1960s and
late 1990s). CBO (2001) estimates TFP growth in the non-farm business
sector to average 1.4 percent over the next decade, which reflects the
more recent trends.

The effects of capital deepening would, superficially, appear to be
easier to forecast. In the traditional Solow model, capital deepening
raises the level of productivity, not its long-run trend growth rate.
The rate of technical progress (TFP growth) is viewed as independent of
capital deepening, and capital deepening cannot increase indefinitely,
as larger and larger shares of output will be absorbed maintaining the
ever-expanding capital stock, ultimately leaving no resources to
consumption. In this view, the impact of capital deepening on
productivity growth will ultimately fade to zero.

More recent thinking in the "new growth" literature is
less pessimistic. In some new growth models, the growth of technical
progress depends directly on the capital-labor ratio. (26) Even in the
traditional view, the transition to the higher productivity level will
yield a lengthy period of higher productivity growth rates, and
reallocation of capital across industries could yield higher aggregate
productivity for some time. Finally, the budget constraint limiting the
growth possibilities of capital deepening in the neoclassical model is
much less binding in the current environment. The budget constraint
involves an ever-increasing share of nominal output being spent on
replacements for the swollen capital stock, leaving few resources for
other activities. (27)

We are in a situation where the price of investment goods is
falling, however, meaning that the higher levels of real investment
spending necessary to maintain and expand the higher capital stock can
be obtained with minimal increases in nominal investment spending
(Macroeconomic Advisors (1999)). Thus, it appears that the contribution
of capital deepening to productivity growth will be sustainable for
years to come, as long as the relative price of investment goods
continues to fall. While this does not lead to a balanced growth
equilibrium, it may be an appropriate representation of the current
economic forces. Moreover, Jorgenson and Stiroh (2000) suggest that the
official price data may understate the true quality gains in computer
software and telecommunications equipment, which would lead to an
overstatement of true inflation, and an understatement of true capital
deepening and output growth. These price concerns, however, are less
important for fiscal policy analysis where nominal output growth is the
more relevant factor for future budgetary considerations.

In sum, a continuation of the post-1995 trend of labor productivity
growth of 2.25 percent per year for some years into the future, perhaps
a decade, seems to be a defensible upper-bound estimate of the
sustainable trend growth rate. However, as the experience of the 1970s
and the late 1990s suggests, forecasts of productivity can easily be
wrong.

Conclusions

Productivity growth is clearly a fundamental measure of economic
health and all of the major measures of aggregate labor and total factor
productivity have recently shown improvements after long spells of
sluggishness. If this improved performance continues, strong overall
performance of real growth and low inflation may he sustained, although
the short-run linkage of productivity to real income (and to output,
after the very shortest period) is not as tight as some might expect.

Examination of the sources of productivity growth suggests that a
major source of the better aggregate performance has been the remarkable
surge of the high-technology sector. Faster productivity growth in this
rapidly growing sector has directly added to aggregate growth, and the
massive wave of investment in high-technology capital by other sectors
has been equally important. Improved productivity growth has not been
solely a high-tech phenomenon, but high-technology is clearly the most
prominent factor.

The increased difficulty of measuring economic activity in a period
of rapid technological change may have aggravated chronic problems in
measuring productivity growth in the service sector. It is doubtful,
though, that the worsening of such problems has gravely distorted the
aggregate data, in part because so much of the product of the service
sector is sold as inputs to other businesses, rather than to final
consumers.

Finally, it is possible that recent productivity growth has been
swelled by the strength of aggregate activity. The longer productivity
growth stays strong, however, the less weight should be placed on
cyclical forces and the more optimistic we can be about improvements in
the underlying, longer-term trends.

ACKNOWLEDGEMENTS

We acknowledge the assistance of Donald Rissmiller and Theresa
Waters, and helpful comments from Erica Groshen and seminar participants
at the Federal Reserve Bank of New York.

This paper won the NABE Contributed Paper Award for 2001. It
expresses the views of the authors only and not necessarily those of the
Federal Reserve Bank of New York or the Federal Reserve System.

Charles Steindel is a senior vice president in the research and
market analysis group of the Federal Reserve Bank of New York. He had
been a vice president in the research area since July 1995. He joined
the bank in 1986 and has been an officer since 1990. He holds a B.S.
degree in mathematics from Emory University and a Ph.D. in economics
from Massachusetts Institute of Technology.

Kevin J. Stiroh is a senior economist with the Federal Reserve Bank
of New York, having joined the bank in 1999. Prior to that, he had been
with the Conference Board and had been a Research Fellow at the Kennedy
School of Government at Harvard University. He is a graduate of
Swarthmore College and holds an M.A. and a Ph.D. in economics from
Harvard.

(1.) As discussed later, labor productivity growth is a good,
although not perfect proxy, for growth in per capita income and rising
living standards.

(2.) This series is usually examined on a four-quarter basis, since
it is quite volatile quarter-to-quarter.

(3.) Fernald and Basu (1999) attribute this apparent regularity to
a combination of pro-cyclical productivity shocks, imperfect competition
and increasing returns, variable input utilization, and resource
reallocations, with the latter two being particularly important.

(4.) See Wolff (1996) for a recent analysis and earlier references.

(5.) There is some controversy about the choice of 1973 as the
break point in the data. Productivity numbers in the first half of the
1970s were clearly heavily affected by the sharp cyclical swings in the
economy and distortions created by the end of the fixed-exchange rate
system, the introduction and removal of wage and price controls, and the
runup in energy prices. For the purposes of this paper the
"traditional" 1973 date, which coincides with the start of the
1973-75 recession, is suitable, but it should not be blindly accepted
for serious statistical analysis. As we will note later in the paper,
the actual existence, much less the precise date, of a break point in
the data in the 1990s remains somewhat controversial. See Filardo (1995)
for an early discussion of the productivity revival.

(7.) For instance, one clearly needs a great deal of labor market
information to compute the number of part-time workers who equal a
full-time worker.

(8.) Another term is the "Solow Residual" in honor of
Robert Solow, the economist who popularized the concept. The BLS
typically refers to this concept as "multifactor productivity"
(MFP). All three terms are synonymous.

(9.) See Lum, Moyer, and Yuskavage (2000) for details on these
definitions.

(10.) This deflation problem complicates the contention that
productivity in non-financial corporate business is more observable than
that for the overall economy. It is certainly correct that (with some
lag) the income of non-financial corporations is measured well. However,
there are surely significant problems in computing the real value of
goods and services purchased by these corporations, and thus in
computing their real value added and productivity. Most notably,
non-financial corporations are major consumers of services purchased
from financial firms. The problems with deriving price indexes for
financial services are well-known, and recognition of these makes the
non-financial corporate data a bit problematic. The data for the
non-farm business sector as a whole has less of this problem, since
financial firms are part of this larger sector, and the bulk of their
sales are to other non-farm businesses.

(11.) See Lum et al. (2000) for details.

(12.) The empirical evidence rejects the technical assumption of
separability that is required for real value added to provide a valid
index of production (Norsworthy and Malmquist, 1983) and Jorgenson,
Gollop, and Fraumeni, 1987). Basu and Fernald (1995) show that
value-added data can give misleading estimates of production parameters
like the degree of returns to scale.

(13.) See Blinder (1997) and Krugman (1997) for a discussion of the
usefulness of this simple relationship.

(14.) The results are similar with the chained personal consumption
expenditures index.fulness of this simple relationship.

(16.) See Huhen (2001b) and Stiroh (2001b) for a description of how
this dissatisfaction contributed to the emergence of new growth theory.

(17.) The proportionality depends on capital's share of
nominal income, which, under the neoclassical assumptions, equals the
elasticity of output with respect to capital. Note that there is no
restriction that this share remains constant over time; it varies as
businesses change their input proportions and as relative prices change.

(18.) See Jorgenson (1990) for a theoretical discussion and Hulten
(2000) for a more recent review of major issues.

(19.) An efficiency profile shows the effective amount of
investment that remains as an assets ages and loses productive capacity
due to decay and retirement. Equation 2 assumes a geometric decline so
that a piece of one-year old capital is (1-[delta])% as productive as a
new piece, a piece of two-year old capital is [(1-[delta])].sup.2]%
productive as a new piece, etc.

(20.) These constant-quality indices are often estimated from
hedonic regressions. See Wasshausen (2000) for details on computer
prices, Parker and Grimm (2000) for estimates of software prices, and
Triplett (1986) for a discussion of hedonic theory.

(21.) As shown in Hall and Jorgenson (1967), tax factors also play
an important role in determining the cost of capital. We omit this issue
for simplicity.

(22.) For example, the Tornqvist index weights growth rates of
different types of capital using service price shares to estimate the
growth of aggregate capital input.

(23.) There are differences, of course. This largely reflects the
broader output concept used by Jorgenson and Stiroh (2000), differences
in estimates of self-employed workers, and differences in the
construction of capital stocks. See Oliner and Sichel (2000) for a
detailed comparison.

(24.) See Fernald and Basu (1999) for a discussion of the
difficulties of measuring unobserved utilization rates.

(25.) We do not dwell on labor quality projections because these
are relatively straightforward based on demographic assumptions.

(26.) See Stiroh (2001b) for a review of several "new
growth" models that have this feature.

(27.) The deterioration of the Warsaw Pact nations in the 198Os may
be an almost textbook case of such a situation. An extraordinary pace of
capital deepening in these nations after World War II resulted, first,
in a period of rapid growth, followed by stagnation and a collapse in
living standards as more and more of their output was devoted to
maintaining the swollen capital stocks. Of course, nonmarket allocations
of resources and high levels of military spending in these nations
exacerbated the problems.